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Mathematics Supporting High Achievement for Students with Disabilities

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Title: Mathematics Supporting High Achievement for Students with Disabilities


1
MathematicsSupporting High Achievement for
Students with Disabilities
  • Ervin Knezek
  • ervin.knezek_at_esc13.txed.net

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Kinds of Data (Bernhardt)
  • Student Learning
  • Demographic
  • School Processes
  • Perception
  • Work in your table group, what are data sources
    for each?

6
Assessment of Students with Disabilities TAKS to
SDAA II (and LDAA)
7
How did we get here?
8
An example from a district
9
  • Instructional decisions should always inform and
    guide assessment decisions.

10
Differences Between SDAA II and TAKS
  • Larger font size
  • More white space
  • Slightly shorter reading and writing passages
  • More illustrations accompanying passages and test
    items
  • Slightly fewer items on some tests
  • SDAA II assesses ALMOST all the same TEKS as TAKS
    (see SDAA II/TAKS/TEKS Correlation Guide)
  • Differences between TAKS and SDAA II do not
    affect level of TEKS curriculum assessed

11
Blueprints
12
Blueprints
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A Tool
Sorting Cards!
TAKS
SDAA II
14
Develop a Common Vocabulary!
  • Intervention
  • Strategies for strengthening processes for
    learning
  • Does NOT change the content of instruction.
  • Accommodation
  • a change in teaching or learning strategies based
    on the specific needs of a student with a
    disability (e.g., oral testing, highlighted
    textbooks, short answer tests) (strategy to
    bypass a process)
  • Does NOT change the content of instruction.
  • Modification
  • a change in the curriculum of a course (e.g.,
    eliminating one or more of the TEKS or changing
    the grade level of certain TEKS)
  • Changes the content of instruction

15
Understanding the difference
  • Intervention
  • Strengthen
  • Link material to previous learning
  • Chunking
  • Mnemonics
  • Tutoring
  • Accommodation
  • By-pass
  • Copy of notes
  • Recorded text
  • Highlighted text
  • Shortened assignment
  • Modification
  • Change
  • Reduce the number of TEKS to be mastered
  • Off grade level instruction

16
Accommodation
  • Which ones are frequently used?
  • Are they allowable of state assessments?
  • How can they be scaffolded?

17
How do we accommodate?
  • Presentation Accommodations
  • Response Accommodations
  • Timing/Scheduling Accommodations
  • Setting Accommodations

18
Youre not ready
Rigor of content
19
Math Test/Assignment Activity
20
Getting on the Same Page with the TEKS
  • Key vocabulary
  • Language of instruction
  • Level of rigor

21
What Are the Priority Standards?
  • EEssential Most Critical 50 of Objectives
  • IImportant Next 30
  • Important now but master later
  • CCondensed Last 20
  • Scaffolded objectives
  • Less instructional time required
  • Plan for the essential first, never compromise on
    time with essentials
  • The more students are at risk, the more time
    allocated to essentials
  • Focus on essentials for remediation and
    acceleration

22
Consider this
  • When an instruction practice is essential to
    average or above average students, it is critical
    to the struggling or underachieving student.
  • The failure to provide effect instruction has a
    more significantly negative impact.
  • (adapted from Turner, 2005)

23
SDAA II TAKS RPTE Correlation Guide
  • Which Student Expectations (SEs)are assessed on
    each test?
  • Which SEs are assessed on both TAKS and SDAA?
  • What is the content?
  • What is the context?
  • What is the cognitive level?

24
Thinking about instruction
Vary in Intensity, Duration, Purpose
  • There is not a separate pedagogy for struggling
    learners (Turner, 2005)
  • Staff expectations and beliefs influence student
    outcomes
  • Achievement gains are more consistent when
    instruction is
  • structured, explicit, and teacher directed for
    new learning (Darling-Hammond, 1992)
  • at the appropriate level of challenge (Vygotsky)
  • Respectful activities (Tomlinson)
  • at the appropriate level of challenge (Vygotsky)
  • at the appropriate level of challenge (Vygotsky)
  • scaffolded (Chang, 2002)
  • mastered before moving on (Ellis, 1997)
  • repeated
  • presented in discreet steps
  • monitored

25
Mathematics
26
What do we know about characteristics of students
with math problems?(Bryant, 2003)
  • Significant differences on
  • Basic skills
  • Higher order mathematical problem solving

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What do we know about characteristics of students
with math problems?(Bryant, 2003)
  • Skills ranked as most problematic for students
    with learning disabilities and math weaknesses
  • Has difficulty with word problems
  • Has difficulty with multi-step problems
  • Has difficulty with the language of math

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Sound like any of your students?
  • Fails to verify answers and settles for first
    answer
  • Cannot recall number facts automatically
  • Takes a long time to complete calculations
  • Makes "borrowing" (i.e., regrouping, renaming)
    errors
  • Counts on fingers
  • Reaches "unreasonable" answers
  • Calculates poorly when the order of digit
    presentation is altered
  • Orders and spaces numbers inaccurately in
    multiplication and division
  • Misaligns vertical numbers in columns
  • Disregards decimals
  • Fails to carry (i.e., regroup) numbers when
    appropriate
  • Fails to read accurately the correct value of
    multi-digit numbers because of their order
  • and spacing
  • Misplaces digits in multi-digit numbers
  • Misaligns horizontal numbers in large numbers
  • Skips rows or columns when calculating
  • (Bryant, Bryant, Hammill, 2000)

29
SDAA II Mathematics
  • Instructional Levels
  • K
  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10
  • Increased rigor
  • Very few differences from TAKS

Not tested at IL K or 1
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SDAA II Mathematics
  • Some items may include application context and
    extraneous information.
  • Each item will extend across the page rather than
    appear in a multicolumn format.
  • Most items will be in a multiple-choice format
    with four answer choices.
  • There may be a limited number of open-ended
    griddable items.
  • Mathematics charts

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IL 3
IL 5
32
A Tool
  • Charting Progress!
  • Content knowledge
  • Instructional Resources
  • Usage Patterns

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Polygon Tree
34
Charts Side by SideMath volume on charts
Gr. 6
Gr. 7
Gr. 8
Gr. 9
35
IL 8
IL 7
36
SDAA II Mathematics IL 9/10
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Mathematics Intervention (Bryant)
  • Sequencing of instructional skills
  • Controlling difficulty or processing demands of
    task
  • Establishing instructional routines
  • Modeling making use of think aloud
  • Daily assessment of skills, distributed review
    and practice, redundant materials or text
  • Teaching to criterion

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Supporting Students with Disabilities for
Success on SDAA II or TAKS Math
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  • Structure of math text
  • Viewing and representing
  • TEKS vocabulary particularly object naming/math
    vocabulary confusion
  • Deconstruction of passage
  • Number
  • Process
  • Using released tests
  • Paired talk throughs
  • Deconstructing distractors

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Tools and Resources
  • http//www.esc13store.net/
  • TAKS Side by Sides
  • Griddies
  • Charts
  • Assessment of Students with Disabilities Toolkit
    for Leaders
  • TAKS off level
  • Smart Teaching Tools
  • http//www.dcschools.com/TAKS/default.asp
  • Special Connections
  • http//www.specialconnections.ku.edu/

43
Professional Development
  • Planning
  • TEKS
  • Assessment
  • Evaluation

44
Planning Time
  • A focus on the curriculum
  • Assigned tasks demonstrating that teachers are
    sharing materials and resources
  • Common assessments being developed
  • Discussion of student work around a priority
    objective

45
Mathematics
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Gr 3
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Gr 4
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Gr 5
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MATH or READING?
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Gr 6
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Gr 7
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Gr 8
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Gr 9
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Gr 10
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Gr 11
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Meter Means Measure Materials adding machine
tape, scissors, one color tile, unit cube, teddy
bears, links, journal Procedure Make a ruler
using only one color tile, plastic bears, links,
unifix cubes (or cm cube) and a paper strip of
your choice using adding machine tape. ??
Where should the tic marks be? ?? How far apart
are your tic marks? ?? Number your tic marks to
make it easier to read your ruler. ?? What
number should be next to the first tic mark? Why?
?? Use your new ruler to measure 3 things in
your classroom. ?? Write about it. Use pictures,
words, and numbers. TEXTEAMS Rethinking
Elementary School Mathematics Part II Day 9
Section C
62
Traditional Math Vocabulary
  • Listen
  • Copy
  • Memorize
  • Drill
  • Drill should never come before understanding.
  • Principles and Standards
  • Drill may produce short-term results on
    traditional tests, but the long-term effects have
    produced a nation of citizens happy to admit they
    cant do mathematics.

Mathematics is the Science of Patterns and Order
63
The Verbs of Math
  • Explore
  • Investigate
  • Solve
  • Justify
  • Represent
  • Formulate
  • Discover
  • Construct
  • Verify
  • Explain
  • Predict
  • Develop
  • Describe
  • Use

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Which Direction?
  • Closed Task One way and one answer
  • Open-Middle Task More than one
    way or
  • one correct answer

  • Open Ended Task More than one
    way or more than one answer

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What did we see?
  • Most SEs assessed
  • Higher levels of thinking required
  • Complex reading in the content areas
  • INCLUDING lots of content
  • Items asked in better ways
  • Declining performance 3-11

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TEKS
  • Now that I have this information, what should I
    do to prepare students?
  • Teach the TEKS!

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Language ArtsSupporting High Achievement for
Students with Disabilities
  • Ervin Knezek
  • ervin.knezek_at_esc13.txed.net

68
Reading
  • (AND Listening)

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SDAA II - Reading
  • Instructional Levels
  • K
  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10
  • Passage lengths somewhat shorter
  • IL K-1 objectives represent learning to read
    tasks
  • IL 2-8 objectives represent a direct correlation
    with TAKS on content, context, cognitive level

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SDAA II Reading
  • Reading Selections
  • Narrative
  • Expository
  • Mixed (starting at IL 2)
  • Paired (starting at IL 4)
  • Triplets (Starting at IL 9)

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SDAA II Reading IL K
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SDAA II Reading IL 1
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SDAA II Reading IL 2
TAKS!
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SDAA II IL 3 -8
  • Beginning at Instructional Level 3, paragraphs
    are numbered
  • When appropriate, each selection is preceded by a
    title.
  • At Instructional Levels 6, 7, and 8, narratives
    are formatted so that students have the option of
    taking notes.

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SDAA II
TAKS
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SDAA II
TAKS
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SDAA II IL 9
  • Triplet of three published pieces
  • Narrative
  • Expository
  • Viewing and Representing
  • Multiple Choice
  • Open ended items
  • Dictionary

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SDAA II IL 9
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Reading
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Reading Overview
  • Longer passages at all grades
  • More expository text
  • Paired selections except at grade three
  • Narrative, expository, mixed passages
  • LITERARY ELEMENTS
  • New objectives/Student Expectations tested
  • True summary
  • Context
  • Dictionary usage
  • Fact and Opinion
  • Conclude!
  • Graphic organizers
  • Viewing and Representing

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To do
  • TEKS training
  • Struggling readers
  • Struggling writers
  • Three tiered reading instruction
  • DIBELS
  • Strategic instruction

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Reading TAAS v. TAKSInstructional Strategies to
Reconsider
  • Short passages
  • Over reliance on key words
  • Single passage selections
  • Any materials with TAAS summarization, fact and
    opinion, context clues
  • Single meaning vocabulary lessons

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the objectives (gr. 3-8)
  • The student will
  • Demonstrate a basic understanding of culturally
    diverse written texts
  • Apply knowledge of literary elements to
    understand culturally diverse written texts
  • Use a variety of strategies to analyze culturally
    diverse written texts
  • 4. Apply critical-thinking skills to analyze
    culturally diverse written texts

84
Grades 10 11 ELA (reading section)Grade 9
Reading
  • Objective 1
  • Basic understanding of the text
  • Objective 2
  • Knowledge of literary elements and techniques
    as used in texts
  • Objective 3
  • Critical analysis and evaluation of texts and
    visual representations

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Gr 3
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Gr 5
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Gr 8
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Gr 9
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Gr 10
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Scaffold
  • Instructional
  • Teacher does, student watches
  • Teacher does, student helps
  • Student does, teacher helps
  • Study Guides
  • Advance Organizers
  • Graphic organizers
  • Tiered Activities

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A Tool
Think about how to get the right answer. Think
about how to get the wrong answer!
Thinking Thing
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A ResourceSpecial Connectionshttp//www.specialc
onnections.ku.edu/
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Supporting Students with Disabilities for
Success on SDAA II or TAKS Reading
  • Connected text
  • VOCABULARY!
  • Scaffolded materials
  • Cognitive walkthrough
  • Talkbacks
  • Construct of text
  • Paragraph stop points

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Writing and ELA (IL 10)
  • And Speaking

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Writing is important because it
  • Contributes to intelligence.
  • It requires analysis and synthesis of
    information.
  • Develops initiative.
  • The writer must supply EVERYTHING.
  • Develops courage.
  • The writer must give up ANONYMITY.
  • Increases personal knowledge and self esteem.
  • Encourages reading skills.
  • From Donald Graves

The vulnerable writer
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Writing
  • Instructional Levels
  • K/1
  • 2
  • 3/4
  • 5
  • 6/7
  • 8/9

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SDAA II Writing IL K/1
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SDAA II Writing IL 2
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SDAA II IL 2 Writing Rubric
  • Focus and Coherence
  • Organization
  • Development
  • of Ideas
  • Convention

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SDAA II Writing IL 3/4 through 8/9
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SDAA II Writing Rubric
  • Focus and Coherence
  • Organization
  • Development
  • of Ideas
  • Voice
  • Conventions

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SDAA II Revising and Editing
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SDAA II ELA IL 10
  • Triplet
  • Narrative
  • Expository
  • Viewing and Representing
  • Writing prompt
  • Student must be on level in both reading and
    writing

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Writing
  • Voice
  • Focus
  • Writing in any mode
  • Revision and editing

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Writing TAAS v. TAKSInstructional Strategies to
Reconsider
  • Formula approaches
  • Over reliance on key words
  • Any TAAS practice materials

111
guidelines for writing
  • Student selects approach
  • Must use standard English prose
  • Four point scale
  • Focused, holistic scoring using a rubric
  • Use of standard English integral part of rubric
  • Expectations appropriate for grade level and
    testing situation

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the writing TEKS
  • Were organized to ensure that at each grade level
    students acquire the writing skills they will
    need for success in the next grade.
  • Even though only some writing TEKS will be
    tested, ALL TEKS must be taught to ensure that
    students receive a solid program of writing
    instruction.

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writing
In order for students to be successful writers,
writing must occur at every grade level, not
merely at the tested grades. -Introduction to
TAKS
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guidelines for writing
  • Student selects approach
  • Must use standard English prose
  • Four point scale
  • Focused, holistic scoring using a rubric
  • Use of standard English integral part of rubric
  • Expectations appropriate for grade level and
    testing situation

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Revising and Editing
  • Whats the difference?

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In revision you When editing you
  • Substitute
  • Add
  • Delete
  • Reorder words, phrases, sentences, ideas and/or
    sections in your draft.
  • Make your writing ready for publication by
    focusing on conventions and mechanics such as
  • Punctuation and capitalization
  • Spelling
  • Sentence Syntax
  • Paragraph structure

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Gr 4
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Gr 7
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Gr 10
It all looks right! Spelling issues!
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Supporting Students with Disabilities for
Success on SDAA II or TAKS Writing
  • Multiple journal writing opportunities
  • Joke telling
  • Connections with reading passages
  • Multiple story telling opportunities
  • Peer review
  • Emphasis on voice
  • Structuring revising and editing based on high
    success opportunities

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A Tool
  • The student sample

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Expository Text (Quinn)
  • Science
  • Social Studies
  • Mathematics

8
127
You Cant Tutor What HasntBeen Taught
  • You cant tutor what hasnt been taught
  • You cant tutor what hasnt been taught
  • You cant tutor what hasnt been taught
  • You cant tutor what hasnt been taught
  • You cant tutor what hasnt been taught
  • You cant tutor what hasnt been taught
  • You cant tutor what hasnt been taught

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The Model
  • Rigorous state Standards that raise
    expectations
  • Curriculum and benchmarks aligned to state
    standards
  • Quality, on-going professional development for
    teachers who support and teach reading
  • Resources to support new instructional strategies
    and classroom management strategies
  • Informal classroom diagnostic assessment for math
    and reading growth
  • STATE TEST ALIGNED to STANDARDS

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Teacher led intervention
  • Find and use ALL data
  • Do analysis for strength and weakness
  • Prioritize needs
  • Set goals Brainstorm specific strategies
  • Results indicators
  • Action Plan

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Assessment (Quinn, 2004)
  • Summative Assessment External Reporting
  • Scorekeeping
  • Broad data for identifying specific populations
  • Program evaluation and budget indicators
  • Formative Assessment Internal Reporting
  • Intervention Do something differently,
    immediately (STOP Spray and Pray!)
  • Progress monitoring over time for individual
    students
  • Data used to plan next move for instruction
    (lesson design)
  • Getting a Grade Comfort the troubled, trouble
    the comfortable
  • Public relations
  • A,B,C,D,F Coin of the realm

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Students with Disabilities
  • Incomplete beginning reading instruction
  • Serious vocabulary deficit
  • Very limited knowledge of text structure
  • Misconceptions about fluency
  • Lack of meaningful early comprehension assessment

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The three most important words for the struggling
reader
  • VOCABULARY
  • VOCABULARY
  • VOCABULARY
  • Words-words-words-words-words-words-words-words-wo
    rds-words-words-words-words-words-words-words-word
    s-words-words-words-you get it!!!!

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What Words to TeachBringing Words to LifeROBUST
Vocabulary InstructionIsabel Beck ,Nancy MacKowen
  • First tier words Words that you wish students
    knew, hope they can get, but you dont have time
    to teach.
  • Second tier words High utility words that they
    need to know in your class, and everyone elses.
  • Third tier words Extremely specific words in your
    content area that require considered, deliberate
    and in depth instruction.

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Three Muscles (Quinn, 2004)
  • Early Language Experience
  • Phonemic awareness and concept development
  • Vocabulary, academic language and alphabetic
    principle
  • Decoding muscle
  • Three ways of getting meaning off the page
  • (1)phonicsprimary decoding strategy
  • (2)semantics and vocabulary
  • (3) syntax and structure
  • Fluency muscle
  • Reads a lot of words fast w/ comprehension
  • Class libraries of high-interest content related
    articles
  • Every day, every reader reading at a level of
    success of self-selected quality literature
    (fiction or non-fiction)

intentional thinking during which meaning is
constructed through interactions between the text
and the reader (Harris Hodges,1995)
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Testwiseness An Important Piece of a
Comprehensive Intervention Strategy
  • On-going, sustained test readiness and rehearsal,
    i.e. testwiseness
  • Phonics instruction for those who received
    hit-or-miss decoding during whole language
    approach analyze spelling errors
  • Build fluency with an every day, every child
    reads at a level of success approach assess for
    oral expression, pace and accuracy
  • Use regular non-fiction writing events to teach
    science soc. studies syntax high-level
    comprehension objectives

136
Teaching Comprehension Directly
  • Monitor the use of the strategy
  • Offer less coaching as less is called for
  • Ask what strategy they are using why, therefore
    bringing the strategy to the students awareness
  • Give students continued opportunity to observe
    more modeling
  • Provide multiple and ongoing opportunities for
    students to interact w/others using a variety of
    text

137
How do I teach those strategies?
  • Decide which strategy you want to model and which
    text to use
  • Tell your students which strategy you are going
    to practice while you read
  • Read the passage to the students modeling the
    strategy you are using..think aloud
  • During real reading, give your students multiple
    chances to practice
  • Continue modeling as the genre or text structure
    changes
  • Give students a chance to practice without your
    coaching or support

138
Five Critical Elements for Rapid Growth (Quinn,
2004)
  • Lesson Design
  • Reading Content alignment vertical and
    horizontal teamingELL, Spec.Ed.
  • Assessment driving differentiated instruction
  • Classroom Management
  • Instruction in terms of minutes
  • Collaboration
  • Whole class, small group, think-pair-share,
    indep.
  • Grade Level Meetings
  • Agendas, increased frequency, evidence driven
  • Student specific with proofs of
    instruction/learning
  • The Role of the Literacy Coach

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  • New expectation for ALL learners
  • Interactive learning and discourse for meaning
  • What the brain likes-MULTISENSORY
  • Reading for MATH
  • Analyzing Data
  • Moving from being data rich to analysis poor
  • SOAP
  • Subjective, Objective, Analyze-Assess, Plan
  • ELL, Spec. Ed.

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Struggling Older Reader
  • Incomplete beginning reading instruction
  • Lacks metacognitive strategies
  • Limited prior knowledge
  • Limited word study skills and spelling
  • No text available at level of success
  • No adults modeling reading
  • No history of reading success

141
What should be done?
  • Dedicated developmental reading testing
    preparedness program 5th through 8th
  • Continued professional development for ALL
    teachers in reading intervention 5-12
  • Initiate on-going professional development in
    science, social studies, and math reading
    writing
  • Integrate a testwiseness curriculum for state
    testing programs with strong emphasis on the
    content areas

142
Reader Response
  • Review the story
  • Select a sentence or phrase that lingers
  • Write down two reasons for selecting that
  • Share your sentence and reasons w/others
  • Come to consensus
  • Be prepared to share to group

143
What is being done?
  • Mandatory summer school
  • Same thing, but LOUDER
  • Expensive intervention programs with uneven
    results
  • Teacher training institutions changing reading
    requirements

144
Five Steps to Two Years Growth for One Year of
Instruction
  • Vertical team study of k-8 reading curriculum
    with evidence of student work
  • Phonics training for 3rd through 8th grade
    teachers
  • Vocabulary instruction training geared more
    toward word harvest
  • Ready availability of compelling leveled text
    with conditional assessment
  • Classroom management strategies that provide
    intensity and focus for below level readers

145
Professional Development
  • Planning
  • TEKS
  • Assessment
  • Evaluation

146
Planning Time
  • A focus on the curriculum
  • Assigned tasks demonstrating that teachers are
    sharing materials and resources
  • Common assessments being developed
  • Discussion of student work around a priority
    objective

147
Making use of Teacher Leader TeamsWho is on your
staff?
148
Questions
149
  • Contact Information
  • ervin.knezek_at_esc13.txed.net
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